Up to two million children affected by Typhoon Haiyan are at risk of abuse or trafficking in the aftermath of the devastating storm, aid agencies have said.

The warning came as the government of the Philippines defended its response to what it described as the largest logistic operation in the country’s history.

The Philippines Red Cross and the United Nations believe that the official death toll from the storm is about 10,000, far higher than the 2,275 currently being quoted by the government.

Most of dead are expected to be adults, as children were sent away before the typhoon’s arrival.

Compounding the problem is the fact that families in the overwhelmingly Roman Catholic Philippines are large, with the average rural family having 3.8 children. In the flattened city of Tacloban alone, some 12,000 women are due to give birth in the coming week, according to Save the Children.

“Lone children in disasters are very vulnerable to abuse, exploitation and trafficking,” said Krista Armstrong, Save the Children’s global media manager. “The first few weeks of any disaster are really critical in terms of putting children at risk. We know this from previous experiences.”

After the 2004 Indian Ocean tsunami, unknown numbers of orphaned children were kidnapped in Indonesia and Sri Lanka, both by child trafficking gangs and couples unable to have children themselves. Similar cases occurred after the Haiti earthquake of 2010.

Haiti and Sri Lanka, though, are small island nations, making it easier for children at risk to be monitored. In contrast, the Philippines is a country of more than 7,000 islands and it is impossible to check on all the children displaced by the typhoon.

“The difficulty with this disaster is that it has affected such a huge region and identifying who is most vulnerable is very hard,” said Ms Armstrong. “There are still remote areas that haven’t been reached, so we don’t know how many orphans there are, or how many children are unaccompanied.”

Judging by the numbers standing with their arms outstretched begging by the side of the roads, or simply hunched alone under the debris that was once their homes, those figures are likely to be high.

“There are children scavenging for food all over the city,” said Edwin Horcas, a Save the Children worker who has just returned from Tacloban. “It is horrifying to see children huddling over the few remaining possessions they managed to salvage. I saw so many just staring blankly ahead. The situation appears overwhelming for them and they are traumatised by what they have been through.”

Save the Children is in the process of setting up what it calls “child-friendly spaces”, as well as flying in a child protection specialist.

Nearly a week after Haiyan reduced the homes of some 700,000 people to piles of timber, people left starving and sleeping in the open are increasingly angry.

So dire is the situation in Tacloban and surrounding Leyte province, as well as parts of neighbouring Samar province, that a night-time curfew has been imposed to prevent looting.

Eight people were crushed to death on Tuesday after thousands of desperate survivors stormed a government rice warehouse west of Tacloban. Aid convoys attempting to take relief to the victims have come under regular attack from both suspected communist rebels and starving survivors of the storm.

The almost complete breakdown of law and order in the areas hardest hit by Haiyan is only further hampering a relief operation that the UN’s World Food Programme has described as a “logistical nightmare”.

One column was forced to turn back Wednesday after being attacked as it tried to travel across the San Juanico Bridge that links Tacloban with Samar province.

The Philippines government appears to be in denial about what has become a massive humanitarian crisis.

Reuben Sindac, a police spokesman, insisted that Tacloban and towns such as Guiuan, where Haiyan first made landfall, were not witnessing a near-complete breakdown in law and order.

He claimed that reports of gunshots ringing out daily were misinformation spread by people “in a state of shock”.

Rene Almendras, the cabinet secretary, said he believed the government was “doing quite well”, even as bloated corpses still littered the streets in some areas.

“This is the largest logistic operation in the history of the Philippines, we have never done anything like this before,” he said. “The Filipino resiliency will be proven by this crisis. Maybe somebody from the outside cannot understand the true nature of this country and the realities that can be found on the ground.”

Aid agencies are increasingly anxious about the risk of typhoid, hepatitis and cholera outbreaks, as survivors are forced to drink contaminated water.

“Vaccines and medical supplies are desperately needed and there are real sanitation concerns,” said Kendra Clegg, part of a UN disaster and assessment team that had just returned from Capiz in the isolated northeast of Panay Island.

“The local officials are expecting a high number of casualties,” she said. “The death toll is definitely going to rise.”

For the thousands of people jamming the Tacloban City Astrodome, the great hall with a solid roof was a heaven-sent refuge when Typhoon Haiyan rammed the eastern Philippines last week. Evacuated from their homes along the coast in time, they had a place to hide from the furious winds and gigantic water surge. But along with shelter, their constant companions now are misery and hunger.

It’s been six days since the typhoon struck but no aid has arrived at the Astrodome. Not a single relief worker is in sight.

“What can we do? There’s nothing we can do!” said Corazon Cecleno, a volunteer with the village council who had handed out food stamps to the occupants — stamps for food that has yet to arrive. “We really want to know why the distribution of help is so slow.”

The people staying here find water wherever they can — from a broken water pipe on the side of the road, from a tarp in a former office building nearby. The water tastes bad — salty — but there is nothing else available and they are desperate.

Just as New Orleans residents took refuge in the Superdome during Hurricane Katrina, thousands of Filipinos are squatting here: inside the stadium, in the ruined shops and restaurants that line it, and under tarpaulins on the grass outside.

Maria Consuelo Martinez, 38, is nine months pregnant and jammed in an abandoned restaurant at the dome along with five families. Her naked 2-year-old son, Mark, sits next to her on a piece of plywood. She has only one outfit for him, and it is drying after a wash. Her 5-year-old daughter, Maria, stares vacantly. Sodden laundry hangs from ropes crisscrossing the room. Flies are everywhere and the tiled floor is slick with filth.

Her husband wanders around, begging for food. Some friends found sacks of ocean-soaked rice at a warehouse and gave the family one. They are drying the grains in the sun on a blue tarp, hoping it will be edible, knowing it will be salty. They have a bottle of well water to cook and wash with, but it tastes like the ocean and they aren’t convinced it’s safe. They drink it anyway.

“We have no choice,” says Moses Rosilio, a neighbour who is squatting in the restaurant with Martinez.

Her baby is due by the end of the month. She has no idea where she’ll deliver.

In the wreckage of a discotheque next door, facing the street in front of the stadium, a few men have built a small fire to cook noodles. The pot will need to feed a dozen people today.

Nearby, Vicky Arcales, 38, uses a hand-crank charger for her mobile phone. She shakes her arm in exhaustion; she’s been at it for three hours. She knows she won’t get a signal anyway, but charges it nonetheless. Just in case.

Behind her, a family has crafted a makeshift baby cot out of a pink-and-white-striped sheet, strung up by cords. It cradles a month-old boy in a shirt, but no diaper; they have none, and no other clothes. Nor do they have food for his mother, who is starving.

The baby stares up at visitors and urinates, the urine seeping through the sheet onto the floor below. A few feet away, a 1-year-old girl wails, her face covered in a red rash. There is no medicine for her.

Inside the dome, Erlinda Rosales lies on a steel barrier propped atop the railing and stadium seats, next to her grandchildren and great-grandchildren. This is their makeshift bed. They are cooking a little nearby on a small burner borrowed from a friend.

Rosales, 72, is one of the lucky ones: Her family has finally received the first supply of relief food. But it was only because her granddaughter has walked every day to their village council to see if the supplies are there. On Thursday’s walk, the food was finally available. They got 3 kilograms (7 pounds) of rice and three cans of sardines.

“I wonder when they will bring food here,” she says.

Daniel Legaspi has less than Rosales, but more than some other people. The 16-year-old holds up a packet of squeezy cheese, powdered biscuits and cream.

“We don’t have bread, but we have the fillings,” he says with a laugh.